The distance (d) between two points (x₁, y₁) and (x₂, y₂) is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
To find the area of the rectangle, find the distance between the points (sides of the rectangle.
Step 01: Finding the distance between A(-3, 0) and B(3,2).
[tex]\begin{gathered} d_{AB}=\sqrt{(3-(-3))^2+(2-0)^2} \\ d_{AB}=\sqrt{6^2+2^2} \\ d_{AB}=\sqrt{36+4} \\ d_{AB}=\sqrt{40} \end{gathered}[/tex]
Step 02: Finding the distance between B(3,2) and C(4, -1).
[tex]\begin{gathered} d_{AB}=\sqrt{()^2+()^2} \\ d_{AB}=\sqrt{(4-3)^2+(-1-2)^2} \\ d_{AB}=\sqrt{1^2+(-3)^2} \\ d_{AB}=\sqrt{1+9} \\ d_{AB}=\sqrt{10} \end{gathered}[/tex]
Step 03: Find the area of the rectangle.
The area (A) of the rectangle is length * width.
Then,
[tex]\begin{gathered} A=\sqrt{40}*\sqrt{10} \\ A=\sqrt{400} \\ A=20square\text{ }units \end{gathered}[/tex]
Answer: 20 square units.
